## Exam

# MATH 225N Week 7 Assignment / MATH225 Week 7 Assignment - Developing Hypothesis and understanding Possible Conclusion for Proportions (Latest, 2020): Chamberlain College of Nursing | 100 % VERIFIED ANSWERS, GRADE A

MATH 225 Week 7 Assignment / MATH225N Week 7 Assignment - Developing Hypothesis and understanding Possible Conclusion for Proportions: Chamberlain College of Nursing MATH 225N Week 7 Assignment / MATH225 Week 7 Assignment - Developing Hypothesis and understanding Possible Conclusion for Proportions: Chamberlain College of Nursing Identify the null and alternative hypotheses for an experiment with one population proportion Question Devin is a researcher for a pharmaceutical company testing whether a new prescription pain medication causes patients to develop nausea. The medication would have to be scrapped if more than 6% of patients who take the medication develop nausea on a regular basis. Devin randomly selected 461 patients for a clinical trial of the medication and found that 27 of the patients developed nausea on a regular basis. What are the null and alternative hypotheses for this hypothesis test?{H0:p=0.06Ha:p>0.06 First verify whether all of the conditions have been met. Let p be the population proportion for patients taking the medication who develop nausea on a regular basis. 1. Since there are two independent outcomes for each trial, the proportion follows a binomial model. 2. The question states that the sample was collected randomly. 3. The expected number of successes, np=27.66, and the expected number of failures, nq=n(1−p)=433.34, are both greater than or equal to 5. Since Devin is trying to determine whether more than 6% of the patients taking the medication develop nausea on a regular basis, the null hypothesis is that p is equal to 0.06 and the alternative hypothesis is that p is greater than 0.06. The null and alternative hypotheses are shown below. {H0:p=0.06Ha:p>0.06 ________________________________________ Great work! That's correct. Compute the value of the test statistic (z-value) for a hypothesis test for proportion Question A college professor claims that the proportion of students passing a statistics course is 80%. To test this claim, a random sample of 250 students who previously took the course is taken and it is determined that 221 students passed the course. The following is the setup for this hypothesis test: H0:p = 0.80 Ha:p ≠ 0.80 Find the test statistic for this hypothesis test for a proportion and round your answer to 2 decimal places. ________________________________________ Well done! You got it right. ________________________________________ 3.32The proportion of successes is p̂ ==0.884. The test statistic is calculated as follows: z=p̂ −p0p0⋅(1−p0)n√ z=0.884−0.800.80⋅(1−0.80)250√ z≈3.32 Compute the value of the test statistic (z-value) for a hypothesis test for proportion Question A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed. The following is the setup for this hypothesis test: {H0:p=0.05Ha:p<0.05 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. ________________________________________ Test_Statistic=2.01Great work! That's correct. Identify the null and alternative hypotheses for an experiment with one population proportion Question An airline company claims in a recent advertisement that more than 94% of passenger luggage that it lost is recovered and reunited with the customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is convincing evidence in support of the airline company's claim. He randomly selects 315 passengers of the airline whose luggage was lost by the airline and found that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?Correct answer: All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p>0.94. First verify whether all of the conditions have been met. Let p be the population proportion for the airline passengers whose luggage was lost by the airline and were reunited with their luggage within 1 day. 1. Since Hunter is completing a survey where there are two independent outcomes, the proportion follows a binomial model. 2. The question states that Hunter randomly selected the airline passengers whose luggage was lost by the airline. 3. The expected number of successes, np=296.1, and the expected number of failures, nq=n(1−p)=18.9, are both greater than or equal to 5. Since all of the conditions for this hypothesis test have been satisfied, determine the null and alternative hypotheses. Since Hunter is determining whether the proportion for reuniting passengers with their luggage within 1 day is greater than 94%, the null hypothesis is that p is equal to 0.94 and the alternative hypothesis is that p is greater than 0.94. The null and alternative hypotheses are shown below. Yes that's right. Keep it up! {H0:p=0.94Ha:p>0.94 Identify the null and alternative hypotheses for an experiment with one population proportion Question Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. She will change over to this new brand unless the actual germination rate is less than what is advertised. Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test? Correct answer:Correct! You nailed it. {H0:p=0.93Ha:p<0.93 First verify whether all of the conditions have been met. Let p be the population proportion for the germination rate of the new seeds. 1. Since there are two independent outcomes for each trial, the proportion follows a binomial model. 2. The question states that the sample was collected randomly. 3. The expected number of successes, np=70.68, and the expected number of failures, nq=n(1−p)=5.32, are both greater than or equal to 5. Since Kylie is testing whether the germination rate is less than 93%, the null hypothesis is that p is equal to 0.93 and the alternative hypothesis is that p is less than 0.93. The null and alternative hypotheses are shown below. {H0:p=0.93Ha:p<0.93 Identify the null and alternative hypotheses for an experiment with one population proportion Question A politician recently made the claim that 47% of taxpayers from a certain region do not pay any income taxes. Makayla is a journalist for an online media company and is testing the politician's claim for an op-ed. She randomly selects 159 taxpayers from the region to conduct a survey and finds that 73 of them do not pay any income taxes. What are the null and alternative hypotheses for this hypothesis test?Correct answer: {H0:p=0.47Ha:p≠0.47. Correct! You nailed it. First verify whether all of the conditions have been met. Let p be the population proportion for the taxpayers who do not pay any income taxes. 1. Since there are two independent outcomes for each trial, the proportion follows a binomial model. 2. The question states that the sample was collected randomly. 3. The expected number of successes, np=74.73, and the expected number of failures, nq=n(1−p)=84.27, are both greater than or equal to 5. Since Makayla is testing the politician's claim of 47%, the null hypothesis is that p is equal to 0.47 and the alternative hypothesis is that p is not equal to 0.47. The null and alternative hypotheses are shown below. {H0:p=0.47Ha:p≠0.47 Compute the value of the test statistic (z-value) for a hypothesis test for proportion Question A college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors. The following is the setup for this hypothesis test: {H0:p=0.40Ha:p>0.40 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.Correct answers: Test_Statistic=3.06Perfect. Your hard work is paying off